Let us review the construction of [1]}, [2]} adapted to the field theory context.
We are interested in deformations of a Hamiltonian, or more generically, a set of conserved charges, which preserve
localityThis should not be confused with locality of quantum field theory in the Wightman axioms [3]}.
in the sense that the undeformed as well as the deformed Hamiltonian can be written as an integral over a local density \(\mathcal {H}(x)\) :
\(H=\int \mathrm {d}x \,\mathcal {H}(x).\) 
